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Full text of "Men Of Mathematics"

MEN OF MATHEMATICS
world since the year 1900. But already in certain important
sectors a most welcome tendency towards contraction is plainly
apparent. This is so, for example, in algebra, where the whole-
sale introduction of postulational methods is making the sub-
ject at once more abstract, more general, and less disconnected
Unexpected similarities - in some instances amounting to
disguised identity - are being disclosed by the modern attack,
and it is conceivable that the next generation of algebraists will
not need to know much that is now considered valuable, as
many of these particular, difficult things will have been sub-
sumed under simpler general principles of wider scope. Some-
thing of this sort happened in classical mathematical physics
when relativity put the complicated mathematics of the ether
on the shelf.                                 fr
Another example of this contraction in the midst of expan-
sion is the rapidly growing use of the tensor calculus in prefer-
ence to that of numerous special brands of vector analysis.
Such generalizations and condensations are often hard for older
men to grasp at first and frequently have a severe struggle to
survive, but hi the end it is usually realized that general
methods are essentially simpler and easier to handle than
miscellaneous collections of ingenious tricks devised for special
problems. When mathematicians assert that such a thing as
the tensor calculus is easy - at least in comparison with some
of the algorithms that preceded it - they are not trying to
appear superior or mysterious but are stating a valuable truth
which any student can verify for himself. This quality of inclu-
sive generality was a distinguishing trait of Poincare's vast
output.
If abstractness and generality have obvious advantages of
the kind indicated, it is also true that they sometimes have
serious drawbacks for those who must be interested in details.
Of what immediate use is it-to a working physicist to know that
a particular differential equation occurring in his work is solv-
able, because some pure mathematician has proved that it is,
when neither he nor the mathematician can perform the Her-
culean labour demanded by a numerical solution capable of
application to specific problems?
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